Adaptation--Next -- Two very funny and chilling plays, both directed by Mike Nichols' brilliant ex-partner, Elaine May. The first one-acter, written by Miss May, shows the game of life as seen in terms of a TV quiz show. The second, by Terrence McNally (a perverse playwright's perverse playwright, and happily so), is about a 48-year-old man undergoing a humiliating army physical. Gabe Dell and James Coco--two of the best actor-comedians around--play the leads. At the GREENWICH MEWS THEATRE, W. 13th St. (243-6800).

Big Time Buck White--Joseph Tuotti's play, which grew out of the Budd Schulberg Watts project, is about an organization called B.A.D. (Black Alleluia Days) and a handful of its members. The doings of these members--who embrace black culture while simultaneously trying to get a grip on the monetary aspects of white culture -- while setting up for a meeting are howlingly funny and true. When the title character, their leader, arrives to answer race-oriented questions, things get a little stagey. The production, which is graced by what may be the best cast in New York, closes Sunday; do not miss it. At the VILLAGE SOUTH THEATRE, 15 Vandam St. (989-7736).

Boys in the Band--A devastating concoction of humor and biterness centered around a homosexual birthday party. The action and dialogue (by Mart Crowley) are grimly explicit, and the all-new cast (under Robert Moore's flawless direction) should be as good as their original counterparts. Totally engrossing, painful, and should not be missed. At THEATRE FOUR, W. 55th St. (246-8545).

Cabaret--This musical about the degeneration of German society just before Hitler came to power is a heady production emblazoned in the tones of Kurt Weill and George Grosz. Most of the original cast is gone, but the Kander-Ebb score, the Boris Aaronson sets, and Harold Prince's direction--all miraculous--are still there. So is Lotte Lenya, who is as beautiful and gravel-voiced as ever. At the BROADWAY, Broadway at 53rd (247-7992).

Cop-Out--As of now, a blind item (since it is still giving low-priced previews), this work by John Guare (author of last year's "Muzeeka") looks promising. At the CORT, W. 48th St. (CI 5-4289).

Dames at Sea--An ingenious musical spoof of the kind of entertainment Busby Berkeley, Dick Powell, Ruby Keeler and Joan Blondell used to provide during the depression: a lot of fun. The cast includes a lovely girl with a weird voice who goes by the name of Bernadette Peters. At the BOUWERIE LAND THEATRE, 330 Bowery at 2nd St. (674-6060).

Dionysus in '69--Richard Schechner's strange and fascinating version of Euripides' "The Bacchae." At the PERFORMING GARAGE, 33 Wooster St. (WA 5-8712).

Fiddler on the Roof--Now in its fifth year and still in great shape, this powerful Stein-Bock-Harnick-Robbins drama weaves Sholom Aleichem's "Tevye" stories into a panoramic view of the breakdown of tradition in Russian-Jewish society. Harry Goz is the present Tevye, and well up to snuff. At the MAJESTIC, W. 44th St. (246-0730).

Frankenstein--Tonight and Saturday the Living Theatre gives its final performances in America for a while. This may not be the best of their productions and you may hate Julian Beck's troupe anyway--but their antics are worth looking at, at least once. At the BROOKLYN ACADEMY, 30 Lafayette Ave. (ST 2-2434).

The Great White Hope -- James Earl Jones' performance as black prize-fighter Jack Johnson is awe-inspiring--and makes a visit to this production worthwhile. But the play (by Howard Sackler) is generally awful and sometimes offensive -- unfocused, full of wretched excesses, and sociologically more pertinent to the forties than the sixties. Edwin Sherin's direction isn't much either, nor is the supporting cast--with the exception of Lou Gilbert as a much-tormented manager. At the ALVIN, W. 52nd St. (757-8646).

Hadrian VII--Alec McCowen's performance as a neurotic-intellectual-homosexual who dreams he becomes Pope is every bit as great as everyone says it is. Peter Luke's script is solid, entertaining, and happily devoid of philosophical pretentiousness. At the HELEN HAYES, W. 46th St. (246-6380).

Hair--A hippie "Hellzapoppin" with a lot of spirit and a nice score firmly based in the vocabulary of early rock. Only when the authors try too hard to explain to our parents what the new culture is all about do things become a little thick. Tom O'Horgan is the director, and the nice cast includes Barry McGuire and the nice Heather MacRae. At the BILTMORE, W. 47th St. (582-4340).

Inner Journey--Hardly great, but still an interesting play by James Hanley. Jules Irving directed and the redoubtable Michael Dunn is in the cast. At THE FORUM, Lincoln Center, W. 65th St. (EN 2-7618).

In the Matter of J. Robert Oppenheimer--A quasi-documentary by Heiner Kipphardt about the hearing in which Dr. Oppenheimer lost his security clearance. Hebert Berghof is in it and so is Joseph Wiseman (in the title role), an actor who never ceases to amaze. At the VIVIAN BEAUMONT, Lincoln Center, W. 65th St. (362-7216).

Invitation to a Hanging--A mixed bag with some style from the New York Shakespeare Festival. The play is adapted from a Vladimir Nabokov novel, the cast includes Joe Bova and John Heffernan, and the director is Gerald Freedman. At the PUBLIC THEATRE, 425 Lafayette St. (677-6350).

Jimmy Shine--An incredibly slight and short character sketch by Murray Schisgal. Still, Dustin Hoffman contributes a truly funny portrayal of the title character; and Donald Drifer's sharp staging and John Sebastran's songs also make it all quite pleasant. At the ATKINSON, W. 47th St. (245-3430).

Little Murders--Jules Feiffer's black comedy (which flopped a few season ago on Broadway) in a new and fine production directed by Alan Arkin. It's a disturbing and wildly funny work about snipers, obscene phone calls, air pollution, masturbation, hippie religion, and a photographer who takes pictures of shit--among other things. Andrew Duncan and Linda Lavin have just left the cast, but Vincent Gardenia and the stunning Elizabeth Wilson are among those who remain. At the CIRCLE-IN-THE-SQUARE, 159 Bleeker St. (473-6778).

Man in the Glass Booth--An exciting piece of theatre about Nazi and Jewish guilt. It all may not mean much, but Donald Pleasence's performance as an Eichman figure and Harold Pinter's direction must be seen. Robert Shaw, the actor, wrote the play. Jack Warden succeeds Mr. Pleasence after this weekend. At the ROYALE, W. 45th St. (245-5760).

Negro Ensemble Company--A fine company tries its hands at three new one-act plays. At ST. MARKS PLAY-HOUSE, 133 Second Ave. (OR 4-3530).

Peace--A satire on war taken from the Aristophanes play. Funny and with a nice score by a very different theatrical song writer, Al Carmines. At the ASTOR PLACE THEATRE, 434 Lafayette St. (254-4730).

Promises, Promises--Burt Bacharach and Hal David write some of the best and most innovative songs around, but perhaps you might prefer to buy the original cast album rather than go to this somewhat unsatisfactory distillation by Neil Simon of Billy Wilder-I. A. L. Diamond's "The Apartment." At the SHUBERT, W. 44th St. (246-5990).

1776--A lot of heat is being generated by this new, serious, non-patriotic musical about the writing of the Declara- tion of Independence. There are those who love it--and those whose hearts do not quite thrill to the goings-on (which include an animated discussion of Thomas Jefferson's sex life). Still, the cast does include such people as William Daniels and Paul Hecht, and the general style of the piece is supposed to be quite out of the ordinary. At the 46th STREET THEATRE, W. 46th St. (246-4271).

Zorba--A great serious musical about living, loving, suffering and dying. John Kander and Fred Ebb wrote the immensely theatrical score; Joseph Stein did the adaptation from the Kazantzakis novel; and producer director Harold Prince tied it all together with a finesse the likes of which have not been seen since Jerome Robbins' heyday. Herschel Bernardi is the man of Crete and Maria Karnilova is his French lady friend. They have a strong assist from gutsy-voiced Lorraine Serabian, who heads a Greek chorus. At the IMPERIAL, W. 45th St. (265-2412)